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arXiv · 1806.07518

Eakin-Sathaye type theorems for joint reductions and good filtrations of ideals

Kriti Goel·Sudeshna Roy·J. K. Verma
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Abstract

Analogues of Eakin-Sathaye theorem for reductions of ideals are proved for ${\mathbb N}^s$-graded good filtrations. These analogues yield bounds on joint reduction vectors for a family of ideals and reduction numbers for $\mathbb N$-graded filtrations. Several examples related to lex-segment ideals, contracted ideals in $2$-dimensional regular local rings and the filtration of integral and tight closures of powers of ideals in hypersurface rings are constructed to show effectiveness of these bounds.

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Kriti Goel, Sudeshna Roy, J. K. Verma. 2018-06-20. Eakin-Sathaye type theorems for joint reductions and good filtrations of ideals. https://arxiv.org/abs/1806.07518

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